SCIENCE AND PRACTICE. 



359 



the cable resistance ; a, one of the coils of the galvanometer, 



whose resistance is r ; B, the battery, whose electro-motive 



force is E, the intensity in the circuit on the right hand 



being I ; R is the resistance i. 



inserted ; b, the galvanometer 



coil ; B', the battery, whose 



electro-motive force is E', and I 7 



the current in the left-hand 



circuit. Let m and m f be the 



opposite magnetic effects of the 



coils a and b upon the needle Fig. 164. 



suspended between them, when the intensities in the circuits 



are equal. 



The relation is first ascertained by direct experiment, 

 by inserting in x a known resistance, and by measuring also 

 the relation , when e and e r are the electro-motive forces of 



6 



the batteries. This is called determining the constant of the 

 apparatus. A known resistance, W, is inserted, instead of x, 

 in the circuit of a battery, B on the other side the amount 

 of the adjustable resistance with a single element, e r , is varied 

 to R 7 , until the needle rests over zero. 



Then the intensities in the two currents are 



I= W^ C 1 - dl '-FT7 i ' ' (2 



That the needle may take up this position, however, it is 

 necessary that the currents in the circuits be inversely pro- 

 portional to the magnetic effects of the coils. 



J?L - - . (3 



m' ~ ' I 



Inserting the values of I and I', given by (1 and (2 in this 

 equation, 



m 



B' 



And if e = e that is to say, a similar electro-motive force 

 be taken on each side, in measuring the constant, 



